I have always had problems inserting images here using URLs from gyazo. I am not sure if the problems if with gyazo, drupal or both.
Here is an example at gyazo:

https://gyazo.com/a063116db5bf1ebf0091e7b6c0b72d1a

Click the share icon and then "copy direct link". That puts the URL to the image in the clip board.
I try to insert the image in a post here, but it then always asks for login credentials!?
I cancel and again click "copy direct link" and again insert the link in my post. It usually works the 2nd time, although I sometimes have to do it three times...